High-resolution Interferometric Diagnostics for Ultrashort Pulses

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3. PHASE RECONSTRUCTION ALGORITHM FOR MULTIPLE SPECTRAL SHEARINGINTERFEROMETRY(a)2(b)2(c)SNN200015001000500200015001000500334456576505 10 15 20 25 30Ω 2 /ΩFigure 3.6: (Color online) Contour plots of noise suppression factor S vs number of samplingpoints and shear ratio for (a) two shears and (b) three shears, with the third shear chosen accordingto the text. (c) Noise suppression factor vs shear ratio for N = 1024 for two shears (blue) and threeshears (red dashed).86
3.9 Numerical comparison of single- and multi-shear retrieval|E |42(a)|D|010.50(b)10∠D/π−1|D|10.50(c)2.2 2.3 2.4 2.5ω (rad/fs)10∠D/π−1Figure 3.7: (Color online) (a) Spectrum of a two-lobed pulse (blue, solid) and spectrally shearedreplicas with small (red, dashed) and large (green, thick line) shears. (b) and (c): Amplitude (blue)and phase (red, dashed) of interference product for the small (b) and the large (c) shear. Thevariation of the interference products with a peak SNR of 50 is shown by the shaded area.phase retardation of π/2 was then applied to the higher frequency lobe. I compared a single shearreconstruction with Ω ≈ 3.14mrad/fs with a two-shear reconstruction with Ω 1 = Ω and Ω 2 = 8Ω ≈25.1mrad/fs. The pulse spectral amplitude and phase are shown in Fig. 3.8(a).Each interferogram D(ω) was contaminated with additive white Gaussian noise with RMS amplitudeequal to 2% of the peak signal amplitude for the single shear case and 4% in the doubleshear case to emulate the worst-case scenario for multi-shear with sequential acquisition. A randomabsolute phase, uniformly distributed over [0,2π), was also added to each interferogram. Thealgorithm of section 3.5 was used for the double shear whilst standard concatenation was used forthe single shear case. Having determined the phase, I reconstructed the complex envelope usingthe spectral intensity of the unknown pulse. The entire process was repeated 1000 times toproduce an ensemble of reconstructions so that the precision could be examined. Once this ensemblewas computed, it was necessary to remove ambiguous zeroth and first order phase fromeach reconstruction so that only fluctuations of higher order would affect the statistics. To do this,87
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High-resolution InterferometricDiag
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AcknowledgementsMy supervisor Ian W
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6 High-harmonic generation 1256.1 D
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List of acronymsADK Ammosov, Delone
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Definitions and symbolsAll Fourier
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1. INTRODUCTIONprofile in space as
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2 BackgroundThis dissertation prese
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2.1 Metrology, ultrashort pulses, a
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2.1 Metrology, ultrashort pulses, a
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2.2 Formal introduction to ultrasho
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2.3 Introduction to ultrashort puls
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Page 47 and 48: 2.3 Introduction to ultrashort puls
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Page 75 and 76: 3 Phase reconstruction algorithm fo
Page 77 and 78: 3.1 Motivationration of information
Page 79 and 80: 3.2 Quantitative noise analysis for
Page 81 and 82: 3.3 Nature of the input datato give
Page 83 and 84: 3.4 Sampling and uniqueness of solu
Page 85 and 86: 3.5 Main algorithmfrom all the shea
Page 87 and 88: 3.5 Main algorithmsituation, Γ k ,
Page 89 and 90: 3.5 Main algorithmfor j = 1,2,...,k
Page 91 and 92: 3.6 Implications for the relative p
Page 93 and 94: 3.7 Signal-to-noise ratio cost of a
Page 95 and 96: 3.8 Signal-to-noise ratio benefit o
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Page 103 and 104: 3.10 Summary, critical evaluation,
Page 105 and 106: 4 Experimental implementations of m
Page 107 and 108: 4.1 Sequential acquisition of shear
Page 109 and 110: 4.1 Sequential acquisition of shear
Page 111 and 112: 4.2 Simultaneous acquisition of she
Page 117 and 118: 5 Compact Space-time SPIDERIn this
Page 119 and 120: 5.2 Role of the measurement planetr
Page 121 and 122: 5.3 Analysis of ST-SPIDERof design
Page 123 and 124: 5.4 A common-path re-imaging ST-SPI
Page 131 and 132: 5.5 Experimental exampleRomero [295
Page 133 and 134: 5.6 Effect of miscalibrationy (pix)
Page 135: 5.7 Summary and outlooknow perform
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6. HIGH-HARMONIC GENERATION10080log
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6. HIGH-HARMONIC GENERATIONwhere re
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6. HIGH-HARMONIC GENERATION• Sadd
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6. HIGH-HARMONIC GENERATIONgiven in
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6. HIGH-HARMONIC GENERATIONderivati
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6. HIGH-HARMONIC GENERATIONPhase ma
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6. HIGH-HARMONIC GENERATION30(S31)2
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6. HIGH-HARMONIC GENERATIONwhere W
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6. HIGH-HARMONIC GENERATIONtheir re
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6. HIGH-HARMONIC GENERATIONsmall pi
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7. LATERAL SHEARING INTERFEROMETRY
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8. QUANTUM-PATH INTERFEROMETRY IN H
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9 Summary and outlookThis chapter s
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the vacuum chamber on the laser pul
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A. NOISE AND UNCERTAINTYdomain, so
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A. NOISE AND UNCERTAINTYUsing the i
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B. SIMULATION CODES FOR HIGH-HARMON
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References[1] Rakov, V. & Uman, M.
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REFERENCES247 (1999). 11[63] Stiben
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REFERENCES[127] Gyuzalian, R., Sogo
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REFERENCES[189] Kornelis, W., Biege
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REFERENCES[254] Geindre, J. P., Aud
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REFERENCES[313] L’Huillier, A. &
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REFERENCESPhys. Rev. Lett. 91, 1630
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REFERENCESMarangos, J. In Conferenc
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High-resolution Interferometric Diagnostics for Ultrashort Pulses

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